{
  "id": "1012.5437",
  "version": "v3",
  "published": "2010-12-24T22:01:42.000Z",
  "updated": "2013-06-28T16:01:39.000Z",
  "title": "Zeta functions and Bernstein-Sato polynomials for ideals in dimension two",
  "authors": [
    "Bart Bories"
  ],
  "comment": "19 pages, 8 figures",
  "journal": "Revista Matem\\'atica Complutense 26 (2013), no. 2, 753-772. MR 3068618",
  "doi": "10.1007/s13163-012-0101-3",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "For a nonzero ideal I of C[x_1,...,x_n], with 0 in supp I, a generalization of a conjecture of Igusa - Denef - Loeser predicts that every pole of its topological zeta function is a root of its Bernstein-Sato polynomial. However, typically only a few roots are obtained this way. Following ideas of Veys, we study the following question. Is it possible to find a collection G of polynomials g in C[x_1,...,x_n], such that, for all g in G, every pole of the topological zeta function associated to I and the volume form gdx on the affine n-space, is a root of the Bernstein-Sato polynomial of I, and such that all roots are realized in this way. We obtain a negative answer to this question, providing counterexamples for monomial and principal ideals in dimension two, and give a partial positive result as well.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-28T16:01:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F10",
      "14H20",
      "11R42",
      "14E18"
    ],
    "keywords": [
      "bernstein-sato polynomial",
      "topological zeta function",
      "volume form gdx",
      "loeser predicts",
      "partial positive result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.5437B"
    }
  }
}